ABSTRACT
This chapter aims to summarize/compare various dependence modeling mechanisms and elaborate modeling steps for nonlinear dependencies among power system input random variables (RVs) to hedge realistic decisions in system planning and operation through probabilistic steady-state analysis (PSSA). For a renewable energy reach power system, inputs for load flow analysis include load real and reactive powers, renewable generations. Gumbel Copula has an ability to capture the strong upper tail dependence and weak lower tail dependence and easily the case of independence and positive dependence; thus, it is quite good to fit in the data as a Copula function. Families of Copula highlighting its importance make it easier in selecting suitable Copula functions. Dependence modeling mainly separates the influence of marginal distributions from the dependence structure. In practice, the dependence among input RVs in any probabilistic analysis is rarely linear. The Gaussian Copula is relatively easy to sample, and different levels of correlation between the marginal can be easily determined.
